7/24/2019 ANOVA-Single Factor -- Tukey Test for Differences

http://slidepdf.com/reader/full/anova-single-factor-tukey-test-for-differences 1/5

ANOVA

SINGLE FACTOR 

Tukey Test for Differences

SITUATION:

• Sam!in" From # or more $ou!ations %ase& on a Sin"!e Factor

• No common !ink 'et(een t)e k*t) o'ser+ation from $ou!ation ,

an& t)e k*t) o'ser+ation of $ou!ation -. or #. etc/

• 0ust )a+e same sam!e si1es from eac) ou!ation

• 2a+e &etermine& t)at t)ere ARE &ifferences in t)e means

3UESTION:

4)ic) means &iffer from t)e ot)ers5

E6am!e:

Can (e conc!u&e t)at t)ere are &ifferences in a+era"e 'attery !ife

of 7 &ifferent tyes of note'ook comuter 'atteries5 An& if so. ()ic)

ones &iffer from t)e ot)ers5

T)e Statistica! F*Test:

28:   A 9 % 9 C 9 D 9 E 2,: At !east one of t)ese  ;s &oes not e<ua! t)e ot)ers

Battery lives on the same type of computer  6 were of Type A

 6 were of Type B 6 were of Type C

 6 were of Type D

 6 were of Type E

7/24/2019 ANOVA-Single Factor -- Tukey Test for Differences

http://slidepdf.com/reader/full/anova-single-factor-tukey-test-for-differences 2/5

Go to:TOOLS

Data Analysis

Anova: Sinle !actor 

"ihliht the #loc$ of cells that contains all

%ata && the 6 %ata rows 'plus the la#el row(

an% the five columns 'A):E*(+

Chec$ La#els in first row

Desinate #einnin

of output area

7/24/2019 ANOVA-Single Factor -- Tukey Test for Differences

http://slidepdf.com/reader/full/anova-single-factor-tukey-test-for-differences 3/5

So ()ic) means &iffer from t)e ot)ers5

Since t)ere are t)e same num'er from eac) ou!ation =>? ** (e can use

t)e TU@E aroac)/

Lo( *+a!ue

=/888888888,8B?

Can conclu%e there are %ifferences inthe averae #attery lives

7/24/2019 ANOVA-Single Factor -- Tukey Test for Differences

http://slidepdf.com/reader/full/anova-single-factor-tukey-test-for-differences 4/5

n

,SE-.  =

T)e TU@E Aroac)

T)e Tukey aroac) states t)at any t(o sample means =  / ;s? t)at &iffers

'y a !ot in&icates t)e correson&in"  population means = ;s? &iffer/

T)e Tukey aroac) &efines a !ot as:

2ere:

0SE 9 0ean S<uare Error =foun& on E6ce! rintout?

n"  9 Num'er in eac) "rou =in t)is case >?

< 9 stu&enti1e& ran"e +a!ue ** a num'er from a ta'!e ==a??

t)at &een&s on:

  ** t)e ro'a'i!ity of &ra(in" a (ron" conc!usion =!et;s use /87?

k ** t)e num'er of ou!ations =7 in t)is case?  ** t)e num'er of &e"rees of free&om for t)e error term =-7 in t)is

case?

T)e ta'!e (e use &oes not )a+e a +a!ue for k 9 7. 9 -7. 'ut &oes )a+e a

+a!ue for k 9 7. 9 - ()ic) is < 9 /, ** (e (i!! use t)is +a!ue an&

ut it on t)e E6ce! srea&s)eet

%y E6ce!: First Coy an& $aste t)e A+era"es =  / ;s? an& t)e Grous. in t)at

or&er to anot)er set of ce!!s on t)e srea&s)eet/

7/24/2019 ANOVA-Single Factor -- Tukey Test for Differences

http://slidepdf.com/reader/full/anova-single-factor-tukey-test-for-differences 5/5

n

,SE-.   =

92>HS3RT=D-#>?

No( tye in t)e <*+a!ue an& ca!cu!ate J =ome"a?/

T)us any t(o sam!e means t)at &iffer 'y more t)an ,>/7,88- in&icates

t)at t)e correson&in" ou!ation means &iffer/

%attery E:

,78 *,8 9 ,8 *** cannot conc!u&e a &ifference 'et(een E an& D

,78 * ,-,/>>> 9 -B/#### ** can conc!u&e E &iffers from A =an& C an& %?/

%attery D:

,8 * ,-,/>>> 9 ,B/#### ** can conc!u&e D &iffers from A =an& C an& %?/

%attery A:,-,/>>> * ,88 9 -,/>> ** can conc!u&e A &iffers from C =an& %?/

%attery C:

,88 * K8 9 ,8 *** cannot conc!u&e a &ifference 'et(een C an& %

/,>